Create a single-player server with bots. Make sure the difficulty is on average, and play cbe_trainstation over and over again until you need to take a break or until you earn the achievement.

If you're willing to take my word for it, there is no need to read this section of the guide. Move on to the next. If you have doubts or just want an explanation, well, here you go.

Why bots? Because the bots are incredibly powerful. They don't hold back when it comes to hitting shots or when it comes to instantly flicking 140 degrees from one zombie to another. They will carry you and make this achievement much easier, unlike real players. Unless you are playing with your friends to get this achievement together, real players will get in your way more than anything. Generally speaking, the more non-achievement-hunting players you have on your team, the slower the team will move. Besides, bots / friends won't votekick you when they get left behind because you pressed the elevator button as soon as humanly possible.

Why cbe_trainstation? I have tested all of the vanilla Bomb Escape maps, recorded the time that it takes to complete the missions, including with separate paths, and found out that cbe_trainstation is the shortest map. I have put the times below. Keep in mind that during the recording of this data, I played as Technician, moved through the level as swiftly as possible, hit every button as soon as I got to it, crouched under every door as it was opening, planted the bomb as early as possible, kept the movement nearly perfect along with some bunny hops here and there, took the most optimal path, kept my health at the level of maximum movement speed, and kept zombie movement interruptions to a minimum. The timer ends when the escape cutscene begins and you lose control of your character:

cbe_bunker: ~4:40 (no drop) / ~4:35 (drop)
cbe_office: ~5:20 (door) / ~5:05 (ladder)
cbe_cityblock: ~4:50 (right gate) / ~4:55 (forward gate)
cbe_flatline: ~5:50 (garage door) / ~5:55 (catwalk)
cbe_trainstation: ~4:00 (cargo) / ~4:35 (underground)

As you can see, cbe_trainstation has the shortest possible time if you're running through the level without somehow skipping anything.

• Press every button as soon as possible, including elevators and lifts. Don't wait for anyone.
  
  
• Take corners as tightly as you can without sacrificing movement speed.
  
  
• Try to avoid taking any damage at all before the bomb is planted as to prevent your movement speed from declining. Movement speed doesn't matter as much post-plant.
  
  
• Rather than quitting and creating a new server every time the map changes, press X, then 3, then 5 to change the map back to cbe_trainstation. You can also type "sv_votenext 0" in the console to remove the vote cooldown.
  
  
• The train on cbe_trainstation begins to leave at 0:20 seconds remaining. If you don't think you can make it there before then, type "kill" in the console to save the time from losing.